Land value does not stay constant as density is increased. It goes up.
Sellers are not dumb. If land is the limiting factor, increasing the density of the buildings on the land by 10x will increase the value of the land by 10x as well.
> Land value does not stay constant as density is increased. It goes up.
True. But when you measure the price elasticity of land you find that density doesn't increase land value as fast as it creates space.
This occurs independently of the value of the new units. Consider a town with three occupied units: one for $5,000, one for $4,000 and one for $3,000. A new unit is built for $6,000. A simple example would involve everyone trading up, thereby leaving an unoccupied $3,000 unit on the market, but let's be more realistic. The person in the $5,000 unit doesn't budge, so the $6,000 unit gets discounted to $5,500. Our top-tier renter moves, leaving their $5,000 unit open. This must now compete for the other two renters, and so on, and so forth.
New renters will enter the market, but there is scant evidence that people move to cities to move into specific units. Instead, people choose and city and then find a place. New units more-efficiently use limitedly-available land. The other benefits from density, e.g. environmental efficiency, faster exchange of ideas and the resulting productivity boost, et cetera, are just cherries on top.
Sellers are not dumb. If land is the limiting factor, increasing the density of the buildings on the land by 10x will increase the value of the land by 10x as well.